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10 cards from this deck
rn(cos(nθ)+isin(nθ))r^n(\cos(n\theta) + i\sin(n\theta))rn(cos(nθ)+isin(nθ))
All integers (positive, negative, or zero)
Raised to power nnn: rnr^nrn
Multiplied by nnn: nθn\thetanθ
eiθ=cosθ+isinθe^{i\theta} = \cos\theta + i\sin\thetaeiθ=cosθ+isinθ
2cosθ=eiθ+e−iθ2\cos\theta = e^{i\theta} + e^{-i\theta}2cosθ=eiθ+e−iθ
2isinθ=eiθ−e−iθ2i\sin\theta = e^{i\theta} - e^{-i\theta}2isinθ=eiθ−e−iθ
cos(−θ)+isin(−θ)\cos(-\theta) + i\sin(-\theta)cos(−θ)+isin(−θ)
Equate real and imaginary parts separately
S=a(1−rn)1−rS = \frac{a(1-r^n)}{1-r}S=1−ra(1−rn)
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